I've never heard a corner store called a Deli in NYC unless it sold cold cuts. And Bodega is used more for the independently run stores. NYC has a lot of Duane

I've never heard a corner store called a Deli in NYC unless it sold cold cuts. And Bodega is used more for the independently run stores. NYC has a lot of Duane Reade's / CVS's and they're generally called by name instead of generic corner stores.